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Methodology Procedures

Projects covered include state-owned and private projects in the Infrastructure, Electric Power, Oil Gas (excluding upstream), Water and Waste, and Mining sectors.

Where applicable, a project is considered as such until the end of construction and ramp-up to full capacity (with the exception of mining projects, where the date of commissioning signifies the end of the project). Projects must have a:

a) Start date b) Estimate for completion c) Initial investment estimate

For state-owned projects, initial information about the start date and estimates for completion and investment are taken from original signed contracts, along with addendums and annexes.

If original contracts cannot be obtained, information is taken from public documents, presentations, news articles from BNamericas archives, and external sources.

In cases where contracts are subject to approval by legislators, the start date is the date of the law or legislative approval.

In the case of private projects, information is taken from public sources, such as stock exchange filings, annual reports, company presentations, third party research and press releases.

In judging the timing of investment decisions for private projects, great care was taken to differentiate between large projects receiving environmental approval and proceeding directly to construction, and smaller projects where the investment decision hinges on securing financing.

Best care is taken to ensure that recorded data is correct at the time of entry and that each entry is backed with a relevant source.

The greatest care possible was taken to ensure consistency of information in order make a like-for-like comparison in project costs. Insofar as the figures rely on disclosure by the organization or company responsible, the figures can be considered to be conservative in nature.

No attempt was made to adjust figures for inflation during the course of research or for consideration of the time value of money.

In the case of state-owned projects, validation is carried out where possible with either a member of the consortium, EPC contractor, a relevant state agency or advisors to either party.

Projects costs are measured in US dollars. Where project costs are measured in a local currency, amounts are converted to US dollars at the date of the relevant announcement, signature or report.

The severity of deviation from original estimates is defined according to set criteria.

Changes in scope beyond the start date are not accounted for.

Where guidance is non-specific as to dates for completion, the following is used. Project to be completed by 2018 = December 31, 2017 Project to be completed in 2018 = December 31, 2018

Conversely If the product is −1, then AB = PQ ,

so O AB O PQ (SAS).

Therefore POQ = AOB and so AOP = 90°.

We have now proved the result for lines through the origin.

If we are given two lines anywhere in the plane, we can draw lines through the origin parallel to the given two lines. The gradient of each new line is the same as the gradient of the corresponding original line. So the result holds for lines that do not necessarily pass through the origin.

EXAMPLE

Show that the line through the points A (6, 0) and B (0, 12) is perpendicular to the line through P (8,10) and Q (4, 8).

Solution

Hence the lines are perpendicular.

Find the equation of the line which passes through the point (1, 3) and is perpendicular to the line whose equation is y = 2 x + 1.

Gradient of the line y = 2 x + 1 is 2.

Gradient of a line perpendicular to this line is −.

Thus the equation of the required line is 2 y + x = 7.

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Proofs with coordinate geometry

Coordinate geometry can be used to prove results in Euclidean Geometry. An important aspect of doing this is placing objects on the Cartesian plane in a way that minimises calculations.

EXAMPLE

Prove that the midpoints of a parallelogram bisect each other using coordinate geometry.

Solution

Let the coordinates of the vertices be O (0, 0), A ( a , 0), B ( a + c , d ) and C ( c , d ).

There is no loss in generality in placing the vertices of the parallelogram on the Cartesian plane in this way.

M = N and so the midpoints coincided which means that the diagonals bisect each other.

EXAMPLE

Prove that the diagonals of a rhombus bisect each other at right angles using coordinate geometry.

Solution

Let the coordinates of the vertices be O (0, 0), A ( a , 0), B ( a + c , d ) and C ( c , d ).

Because it is a rhombus all the sides are of equal length.

The product of the gradients of the diagonals = × = .

OA 2 = a 2 and by Pythagoras’ theorem, AB 2 = c 2 + d 2

so a 2 = c 2 + d 2 .

Hence d 2 = −( c 2 a 2 )

Thus the product of the gradients of the diagonals = −1.

EXERCISE 6

In any triangle AB C prove that AB 2 + AC 2 = 2( AD 2 + DC 2 )

Where D is the midpoint of BC .

EXERCISE 7

Prove that set of points equidistant from two given points is a straight line.

EXERCISE 8

Prove that the lines joining the midpoints of opposite sides of a quadrilateral and the lines joining the midpoints of its diagonals meet in a point and bisect each other.

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LINKS FORWARD

Figure 3. Erythrocytes inhibit pneumococcal growth by reactive oxygen species-related mechanism.

S. pneumoniae cells (∼1×10 2 CFU, 10 µl) were added to erythrocytes (5×10 9 cells/ml, 190 µl) with or without 1 mM 2,2′-bipyridyl (iron chelator), 1 mM S-ethyl-ITU (nitric oxide synthase inhibitor), 100 µM EUK8 (synthetic catalytic free radical scavenger), or 150 µM MnTBAP (superoxide dismutase mimetic) for 2 hours at 37°C in a 5% CO 2 atmosphere. Next, each mixture was serially diluted and plated on TS blood agar. Following incubation, CFU values were determined. *Significant difference ( P <0.005) between mean values, as determined with a Mann-Whitney U -test. The experiments were performed 3 times and data are shown as the mean of 6 wells from a representative experiment. S.D. values are represented by vertical lines.

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Gram staining of blood cultures infected with invasive S. pneumoniae bacteria under clinical laboratory test conditions showed that some of the pneumococci became associated with human erythrocytes ( Womens Funky and Fabulous Wedge Boots Joe Browns Free Shipping Prices DUWuWdNQ
). In order to further investigate the invasion of erythrocytes by S. pneumoniae , mixtures of the bacteria and erythrocytes were analyzed in detail using a scanning electron microscope (SEM) and confocal fluorescence microscopy. SEM analysis was performed with human blood samples incubated for 1 hour with unencapsulated S. pneumoniae strain R6 or its encapsulated parent strain D39 ( Fig. 4 B ), which revealed that the organisms adhered to ( Fig. 4 B a , c ) and invaded ( Fig. 4 B b , d ) erythrocytes in human blood, regardless of the capsule phenotype. In fluorescence analysis with confocal microscopy performed with human erythrocytes incubated for 1 hour with S. pneumoniae strain R6 or D39 Z-stack analysis clearly showed that both strains invaded erythrocytes ( Fig. 4 C ).

Figure 4. invasion of human erythrocytes.

A . Gram staining of cultures of blood obtained from a patient with invasive pneumococcal pneumonia. A blood sample was obtained from a splenectomized patient with pneumococcal bacteremia and meningitis. We observed that some of the S. pneumoniae cells in the sample adhered to or invaded erythrocytes. B . SEM analysis of S. pneumoniae in blood. S. pneumoniae cells (arrows) were incubated in human whole blood for 30 minutes at 37°C. Strains R6 and D39 adhered to (a, c) and invaded (b, d) erythrocytes in human blood. C . Confocal fluorescence microscopic analysis of S. pneumoniae strains R6 (a, b) and D39 (c, d) incubated with human erythrocytes for 30 minutes at 37°C. (a, c) Erythrocytes were visualized using Alexa Fluor 594 Phalloidin. S. pneumoniae organisms were stained using SYTOX green. (b) Boxed areas from panel (a), along with x–z and y-z projections. (d) 3D analysis of image from panel (c) showing erythrocytes invaded by S. pneumoniae . D . Rate of S. pneumoniae invasion of erythrocytes. The numbers of invaded bacteria were determined as described in the Experimental Procedures section. *Significant difference ( P <0.005) between mean values, as determined with a Mann-Whitney U -test. The experiments were performed 3 times and data are shown as the mean of 6 wells from a representative experiment. S.D. values are represented by vertical lines. E . Histopathological examinations of infected mice lung tissues. Tissues were excised from sites of infection after 72 hours, then fixed, embedded in paraffin, and stained with hematoxylin-eosin solution. (a) and (b) were obtained from individual mice. Arrows indicate association of S. pneumoniae with erythrocytes. (c) Numbers of bacteria associated with erythrocytes per field. Data shown represent the mean of 10 fields from a representative mouse. S.D. values are represented by vertical lines.

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